Related papers: Hyperparameter Optimization in the Estimation of P…
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and…
We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…
We propose a multistage method for making inference at all levels of a Bayesian hierarchical model (BHM) using natural data partitions to increase efficiency by allowing computations to take place in parallel form using software that is…
Joint utilization of multiple discrete frequency bands can enhance the accuracy of delay estimation. Although some unique challenges of multiband fusion, such as phase distortion, oscillation phenomena, and high-dimensional search, have…
The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…
Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…
A recent novel extension of multi-output Gaussian processes handles heterogeneous outputs assuming that each output has its own likelihood function. It uses a vector-valued Gaussian process prior to jointly model all likelihoods' parameters…
We present a general and scalable framework for the automated discovery of optimal meta-solvers for the solution of time-dependent nonlinear partial differential equations after appropriate discretization. By integrating classical numerical…
Modern epidemiological analytics increasingly use machine learning models that offer strong prediction but often lack calibrated uncertainty. Bayesian methods provide principled uncertainty quantification, yet are viewed as difficult to…
Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the…
We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…
This paper presents a hybrid optimization methodology for parameter estimation of reactive transport systems. Using reduced-order advection-diffusion-reaction (ADR) models, the computational requirements of global optimization with dynamic…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
Hyperparameter selection in continual learning scenarios is a challenging and underexplored aspect, especially in practical non-stationary environments. Traditional approaches, such as grid searches with held-out validation data from all…
Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious…
Hyperparameter optimization (HPO) is generally treated as a bi-level optimization problem that involves fitting a (probabilistic) surrogate model to a set of observed hyperparameter responses, e.g. validation loss, and consequently…
We describe a method for Bayesian optimization by which one may incorporate data from multiple systems whose quantitative interrelationships are unknown a priori. All general (nonreal-valued) features of the systems are associated with…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic k-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based…